Discrete Structures for Computer Science - MCQS

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Question:

Let
m be an integer with m > 1. R on the set of integers is an equivalence
relation if

Select
one:

a.
{(a, b) | a ≡ b (mod m)}

b.
{(a, b) | a ≡ a (mod b)}

c.
{(a, b) | b ≡ b (mod a)}

d.
{(a, b) | b ≡ a (mod m)}

The Correct answer is:

{(a, b) | a ≡ b (mod m)}

Question:

Consider
the statement: ∀ x,y E
Z if both xy and x + y are even, then

Select
one:

a.
both x and y are odd

b.
both x and y are even

c.
x is even and y is odd

d.
x is odd and y is even

The Correct answer is:

both x and y are even

Question:

If
A = {0, 1}, B = {1, 2}, and C = {0, 1, 2} then what of the following isn’t in A
× B × C ?

Select
one:

a.
(1, 1, 0)

b.
(2, 2, 0)

c.
(1, 1, 1)

d.
(1, 2, 2)

The Correct answer is:

(2, 2, 0)

Question:

Let
A, B, and C be sets. Identify the the correct one among the following

Select
one:

a.
None of these

b.
A ∩ (B ∩ C) = (C ∪ B) ∪ A

c.
A ∪
(B ∩ C) = (C ∪ B) ∩ B

d.
A ∩ (B ∪
C) = (C ∩ B) ∩ A

The Correct answer is:

None of these

Question:

Let
f1 and f2 be functions from R to R such that f1(x) = x2 and f2(x) = x − x2.
What are

the
functions f1 + f2 and f1 f2?

Select
one:

a.
x2 and x4 – x3

b.
x and x3 – x2

c.
x3 and x2 – x3

d.
x and x3 − x4

The Correct answer is:

x and x3 − x4

Question:

Determine
for what of the following for “f” is not a one-to-one function:

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